A fiber Bragg grating (FBG) is a periodic modulation of the refractive index of the core of a single mode optical fiber usually written by exposure to UV light. This periodic structure is characterized by a narrow reflective spectral response. The center wavelength λB of the reflection band matches the Bragg condition:λB=2neffΛ,  (1)where neff is the effective index of the guided mode and Λ is the period of the index modulation. The FBG resonance wavelength will vary accordingly with temperature and/or strain changes experienced by the fiber. For a temperature change ΔT; the corresponding wavelength shift is given by:
                                          Δλ            B                    =                                                                      λ                  B                                ⁡                                  (                                                                                    1                        Λ                                            ⁢                                                                        ∂                          Λ                                                                          ∂                          T                                                                                      +                                                                  1                        n                                            ⁢                                                                        ∂                          n                                                                          ∂                          T                                                                                                      )                                            ⁢              Δ              ⁢                                                          ⁢              T                        =                                                                                λ                    B                                    ⁡                                      (                                                                  α                        F                                            +                      ξ                                        )                                                  ⁢                Δ                ⁢                                                                  ⁢                T                            =                                                λ                  B                                ⁢                                  β                  T                                ⁢                Δ                ⁢                                                                  ⁢                T                                                    ,                            (        2        )            where αF is the fiber coefficient of thermal expansion (CTE) and ξ is the fiber thermo-optic coefficient, with values of 0.55 ppm/° C. and 6.7 ppm/° C., respectively. The wavelength shift induced by a longitudinal strain variation ε is given by
                                          Δλ            B                    =                                                                      λ                  B                                ⁡                                  (                                                                                    1                        Λ                                            ⁢                                                                        ∂                          Λ                                                                          ∂                          ɛ                                                                                      +                                                                  1                        n                                            ⁢                                                                        ∂                          n                                                                          ∂                          ɛ                                                                                                      )                                            ⁢              ɛ                        =                                                                                λ                    B                                    ⁡                                      (                                          1                      -                                              p                        e                                                              )                                                  ⁢                ɛ                            =                                                λ                  B                                ⁢                                  β                  ɛ                                ⁢                ɛ                                                    ,                            (        3        )            where pe is the photoelastic coefficient of the fiber (typically, pe=0.22). In the last two equations, βT and βε, are defined as the temperature and strain sensitivities of the FBG, respectively. The usual approximate values for these two coefficients on the C-band are βT=7.25 ppm/° C. and βε=0.76 ppm/λε. The overall Bragg wavelength shift induced by temperature change and/or strain is then given by
                                          Δλ            B                                λ            B                          =                                            β              T                        ⁢            Δ            ⁢                                                  ⁢            T                    +                                    β              ɛ                        ⁢                          ɛ              .                                                          (        4        )            
The simplest method to overcome cross-sensitivity to temperature while measuring strain with FBGs relies on the use of an additional temperature reference, such as a strain-inactive FBG [W. W. Morey, G. Meltz and J. M. Weiss, “Evaluation of a fiber Bragg grating hydrostatic pressure sensor,” in Proceedings of the Eighth International Conference on Optical Fiber Sensors (Monterey, Calif., USA), Postdeadline Paper PD-4.4 (1992)]. Other methods, based on the use of dual wavelength FBG [M. G. Xu, J.-L. Archambault, L. Reekie, and J. P. Dakin, “Discrimination between strain and temperature effects using dual-wavelength fiber grating sensors,” Electron. Lett. 30, pp. 1085–1087 (1994)], FBG and fiber polarization-rocking filter [S. E. Kanellopoulos, V. A. Handerek, and A. J. Rogers, “Simultaneous strain and temperature sensing with photogenerated in-fiber gratings,” Opt. Lett. 20, pp. 333–335 (1995)], non-sinusoidal FBG [G. P. Brady, K. Kalli, D. J. Webb, D. A. Jackson, L. Zhang, and I. Bennion, “Recent developments in optical fiber sensing using fiber Bragg gratings,” in Proceedings of the Fiber Optic and Laser Sensors XIV (Denver, Colo., USA), SPIE 2839, pp. 8–19 (1994)], FBG written in different diameter fiber [S. W. James, M. L. Dockney, and R. P. Tatam, “Simultaneous independent temperature and strain measurement using in-fiber Bragg grating sensors,” Electron. Lett. 32, pp. 1133–1134 (1996)], FBG and long period grating [H. Patrick, G. M. Williams, A. D. Kersey, J. R. Pedrazzani, and A. M. Vengsarkar, “Hybrid fiber Bragg grating/long period fiber grating sensor for strain/temperature discrimination,” Photon. Technol. Lett. 8, pp. 1223–1225 (1996)], FBG and in-line fiber etalon [H. Singh and J. Sirkis, “Simultaneous measurement of strain and temperature using optical fiber sensors: two novel configuration” in Proceedings of the Eleventh International Conference on Optical Fiber Sensors (Hokkaido University, Sapporo, Japan), pp. 108–111 (1996)], and FBG pair written in hi-bi fibers [M. Sudo, M. Nakai, K. Himeno, S. Suzaki, A. Wada, and R. Yamauchi, “Simultaneous measurement of temperature and strain using PANDA fiber grating,” in Proceedings of the Twelfth International Conference on Optical Fiber Sensors (Williamsburg, Va., USA), pp. 170–173 (1997), L. A. Ferreira, F. M. Araújo, J. L. Santos, F. Farahi, “Simultaneous measurement of strain and temperature using interferometrically interrogated fibre Bragg grating sensors”, Optical Engineering 39, pp. 2226–2234 (2000)] have been demonstrated, but they are often too complex and difficult to implement in real world structures. Moreover, besides being not required in all the strain monitoring cases, the measurement of temperature by the referred methods implies the allocation of additional bandwidth to each sensor, therefore limiting the total number of sensors in a given sensing network.
One temperature compensation method relies on subjecting the FBG to additional temperature induced strain. The simplest method of applying temperature dependent strain to an FBG is to attach it to a material with a CTE dissimilar to silica. However, this restricts the adjustment of the FBG sensitivity to the set of discrete values that can be obtained employing available materials. A well-known method of attaining a broad range of effective CTEs, including negative CTE values, is to provide a structure incorporating a proper arrangement of two materials with distinct CTEs [DE3112193, incorporated herein by reference]. A proper design of such a structure can be used for packaging FBGs, allowing for continuous adjustment of the FBG temperature sensitivity. The particular case of a thermal operation employing this concept has been the focus of several patent applications [WO 01/67142 A2, U.S. Pat. No. 6,393,181 B1; both incorporated herein by reference]. These methods require the use of two materials having different CTEs.